Overall conclusions

The findings from the experimental and numerical investigations have given new insight into the UNDEX induced whipping response of a submerged platform. The following conclusions were drawn based on the outcomes of the presented investigations and are summarised here in relation to their respective research questions.

6.2.1. Effects of UNDEX variables on whipping

Both the experimental and numerical investigations considered what effects the variables of the UNDEX charge size, stand-off distance and location have on a platform’s whipping response. The conclusions of these are summarised below:

1. It was found that the UNDEX charge size, and the resulting pulsating bubble size, period, and frequency, affected the bending modes excited during the whipping response. The most severe whipping occurred when the bubble pulsation frequency was similar to the first bending mode response of the platform. In addition, it was found that the larger charge sizes tended to excite lower bending modes, while the smaller charge excited higher modes and the response from the smaller charge was generally localised near the charge stand-off location. This suggested that to induce a global whipping response, sufficient explosive energy and/or a large enough bubble was required. The investigations identified that relative bubble sizes of 3.8 ≤ λ ≤ 4.5 were sufficient to induce a global response, while a relative bubble size of λ = 2.5 was not.

2. The UNDEX stand-off distance from the hull had no effect on the bending modes that were excited during whipping for bubble proximities of 1.40 ≤ γ ≤ 2.00 and relative sizes of

2.5 ≤ λ ≤ 4.5. The stand-off distance only affected the severity, where a closer stand-off distance increased the whipping response. It was found that the percent increase in the whipping response was consistent for all similar charge size and stand-off location scenarios, where the response from events of the same charge size and stand-off location at γ = 1.40 was approximately 55 % higher than their counterparts at γ = 2.00. These values are likely to be specific to the test platform, but it is suggested that characterisation of these responses at different bubble proximities for a specific platform could be utilised as a rapid assessment tool to predict a platform’s survivability against UNDEX threats. This has the potential to enhance operational decision making.

3. The stand-off location had the most significant effect on the UNDEX induced whipping response and results from both investigations demonstrated that whipping is not a general response, but can take different forms depending on where the UNDEX stand-off is located in relation to the platform’s first bending mode shape. These are detailed further in Section 6.2.3.

6.2.2. Assessment methods for UNDEX induced whipping

The DAA BEM was explored as an analysis tool for the UNDEX induced whipping response of a submerged platform. The following conclusions were drawn from a review of existing methods and numerical validation of the DAA method to experimental results:

1. The numerical DAA BEM was demonstrated as a capable assessment method for an UNDEX induced whipping analysis for bubble proximities 1.40 ≤ γ ≤ 2.00 and relative sizes of 2.5 ≤ λ ≤ 4.5. This method worked on the assumption of minimal bubble-structure interaction and for cases where the bubble is significantly affected by the platform response (or vice-versa) alternative analysis methods should be sought. Full fluid-structure interaction modelling has great potential to overcome this constraint, but current computation costs (in terms of both budget and time) make this difficult to access for most industries.

2. It was shown that the results from both experimental and numerical investigations can be used to characterise a platform’s whipping response. This information may be used to develop rapid assessment tools for a platforms survivability that can be used directly by the operators, potentially enhancing the decision making process in regards to UNDEX threats. 3. Comparisons of the numerical shock-only loading study to experimental results demonstrated that using analysis methodologies based only on the shock response severely under-predicted the critical and general whipping responses by 39 – 54 %, but compared well for resilient whipping response scenarios. Based on these comparisons, it is strongly recommended that shock response analysis methodologies should not be used for a whipping response analysis.

6.2.3. Characterisation of whipping responses and regimes

In the past, whipping has been considered as a general platform response due to transient loading. Through these investigations it has been shown for the first time that the UNDEX induced whipping response can vary significantly, even when the UNDEX charge size and stand-off distance is the same. Based on observations from comparisons of the bubble impulse and the peak whipping response, three unique UNDEX induced whipping responses were defined:

1. The most severe whipping responses occurred when the UNDEX stand-off location was located near the anti-node of the first bending mode shape of the platform. This was especially severe when the bubble pulsation frequency was close to the first bending mode frequency, which caused the response to be dominated by the first bending mode. A whipping response of this form may be defined to as the critical whipping response due to the risk it poses to the overall survivability of a platform.

2. The whipping response was found to be far less severe when the UNDEX stand-off location was near the node of the first bending mode shape, with peak whipping response strains that were 58 % to 71 % lower than similar events at the anti-node stand-off location. The responses at this stand-off location had an absence of the first bending mode in the overall response and the platform had an apparent resistance to the loading from the pulsating bubble. Based on these observations, whipping responses similar to this may be defined to as the resilient whipping response. This form of whipping could potentially be used to the advantage of a platform’s survivability, if the stand-off location of an UNDEX threat can be influenced to induce this response.

3. In between the nodes and anti-nodes of the first bending mode shape, varying degrees of the first three bending modes contributed to the overall UNDEX induced whipping response of the platform. This may be defined to as the general whipping response. Under this condition, the interaction of multiple modal responses may cause the largest whipping response to occur away from the stand-off location, making it difficult to detect without a global response assessment method.

The knowledge of these different elastic whipping response behaviours due to near-field, non- contact UNDEX will allow for better design and analysis to be performed on current and future maritime platforms, to ensure they can meet the challenges of their high-risk environment. Through limited extrapolation of these different whipping responses, four whipping analysis regimes were identified:

1. Far-field elastic

2. Near-field, non-contact elastic 3. Non-contact plastic

4. Contact damage

The conducted investigations suggest that these regimes are valid for bubble proximities of

1.40 ≤ γ ≤ 2.00 and relative sizes of 2.5 ≤ λ ≤ 4.5; however, the absolute limits of these regimes were not identified and are a promising area of further work.